A244452 Primes p such that p^2-2 and p^2+4 are also prime (i.e., initial members of prime triples (p, p^2-2, p^2+4)).

3, 5, 7, 13, 37, 47, 103, 233, 293, 313, 607, 677, 743, 1367, 1447, 2087, 2543, 3023, 3803, 3863, 4093, 4153, 4373, 4583, 4643, 4793, 4957, 5087, 5153, 5623, 5683, 5923, 6287, 7177, 7247, 7547, 7817, 8093, 8527, 9133, 9403

Offset: 1

Author

Felix Fröhlich, Jun 28 2014

Keywords

• nonn

Comments

Intersection of A062326 and A062324.

Examples

			3 is in the sequence since it is the first member of the triple (3, 3^2-2, 3^2+4) and the resulting values in the triple (3, 7, 13) are all prime.
		

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..242507 (all terms up to 10^9)

Crossrefs

Cf. A022004, A073648, A098413.

Programs

Mathematica

Select[Prime[Range[1200]],AllTrue[#^2+{4,-2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 28 2018 *)

PARI

forprime(p=2, 10^4, if(isprime(p^2-2) && isprime(p^2+4), print1(p, ", ")))